W. Lang, Oct 10 2007


a(n,m) tabl head (triangle) for  A134134 (called S2'(2))

Obtained after summing the partition array A134133 over the numbers with fixed m (part number).



    n\m          1         2        3       4       5      6     7     8    9   10 ...


    1            1         0        0       0       0      0     0     0    0    0

    2            2         1        0       0       0      0     0     0    0    0

    3            6         2        1       0       0      0     0     0    0    0

    4           24        10        2       1       0      0     0     0    0    0

    5          120        36       10       2       1      0     0     0    0    0

    6          720       204       44      10       2      1     0     0    0    0

    7         5040      1104      228      44      10      2     1     0    0    0

    8        40320      7776     1272     244      44     10     2     1    0    0

    9       362880     57600     8760    1320     244     44    10     2    1    0

   10      3628800    505440    63936    9096    1352    244    44    10    2    1
    .
    .
    .

 The row sums give A077365: [1, 3, 9, 37, 169, 981, 6429, 49669, 430861, 4208925].

 The alternating row sums give A134135: [1,1,5,15,93,551,4129,33607,312929,3179343,...].


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